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\begin{document}


stavový vektor je:
$$
\xi=
\begin{pmatrix}
\dot{y}\\
\dot{x}\\
\psi\\
\dot{\psi}\\
Y\\
X
\end{pmatrix}
$$
vstupní vektor je:
$$u=
\begin{pmatrix}
\delta_{f}\\
s_{f,l}\\
s_{f,r}\\
s_{r,l}\\
s_{r,r}
\end{pmatrix}
$$
rovnice pak jde zapsat:
\begin{align*}
\ddot{x}&=&&\dot{y}\dot{\psi}+\frac{\left(F_{x_{f,l}}+F_{x_{f,r}}+F_{x_{r,l}}+F_{x_{r,r}}\right)}{m}\\
\ddot{y}&=&&-\dot{x}\dot{\psi}+\frac{\left(F_{y_{f,l}}+F_{y_{f,r}}+F_{y_{r,l}}+F_{y_{r,r}}\right)}{m}\\
\dot{\psi}&=&&\dot{\psi}\\
\ddot{\psi}&=&&\frac{a\left(F_{y_{f,l}}+F_{y_{f,r}}\right)-b\left(F_{y_{r,l}}+F_{y_{r,r}}\right)+c\left(-F_{x_{f,l}}+F_{x_{f,r}}-F_{x_{r,l}}+F_{x_{r,r}}\right)}{I}\\
\dot{Y}&=&&\dot{x}\sin{\psi}+\dot{y}\cos{\psi}\\
\dot{X}&=&&\dot{x}\cos{\psi}-\dot{y}\sin{\psi}
\end{align*}

pro první rovnici platí
\begin{align*}
\dot{y}\dot{\psi},\ \begin{pmatrix}\dot{\psi}&0&0&\dot{y}&0&0\end{pmatrix}
\end{align*}
\end{document}